def init_points(self):
uv_surface = self.uv_surface
full_nu, full_nv = uv_surface.resolution
part_nu, part_nv = self.resolution
u_indices = np.linspace(0, full_nu, part_nu).astype(int)
v_indices = np.linspace(0, full_nv, part_nv).astype(int)
points, du_points, dv_points = uv_surface.get_surface_points_and_nudged_points(
)
normals = uv_surface.get_unit_normals()
nudged_points = points + self.normal_nudge * normals
for ui in u_indices:
path = OpenGLVMobject()
full_ui = full_nv * ui
path.set_points_smoothly(nudged_points[full_ui:full_ui + full_nv])
self.add(path)
for vi in v_indices:
path = OpenGLVMobject()
path.set_points_smoothly(nudged_points[vi::full_nv])
self.add(path)
def __init__(
self,
func: Callable[[np.ndarray], np.ndarray],
color: Color | None = None,
color_scheme: Callable[[np.ndarray], float] | None = None,
min_color_scheme_value: float = 0,
max_color_scheme_value: float = 2,
colors: Sequence[Color] = DEFAULT_SCALAR_FIELD_COLORS,
# Determining stream line starting positions:
x_range: Sequence[float] = None,
y_range: Sequence[float] = None,
z_range: Sequence[float] = None,
three_dimensions: bool = False,
noise_factor: float | None = None,
n_repeats=1,
# Determining how lines are drawn
dt=0.05,
virtual_time=3,
max_anchors_per_line=100,
padding=3,
# Determining stream line appearance:
stroke_width=1,
opacity=1,
**kwargs,
):
self.x_range = x_range or [
floor(-config["frame_width"] / 2),
ceil(config["frame_width"] / 2),
]
self.y_range = y_range or [
floor(-config["frame_height"] / 2),
ceil(config["frame_height"] / 2),
]
self.ranges = [self.x_range, self.y_range]
if three_dimensions or z_range:
self.z_range = z_range or self.y_range.copy()
self.ranges += [self.z_range]
else:
self.ranges += [[0, 0]]
for i in range(len(self.ranges)):
if len(self.ranges[i]) == 2:
self.ranges[i] += [0.5]
self.ranges[i][1] += self.ranges[i][2]
self.x_range, self.y_range, self.z_range = self.ranges
super().__init__(
func,
color,
color_scheme,
min_color_scheme_value,
max_color_scheme_value,
colors,
**kwargs,
)
self.noise_factor = (noise_factor if noise_factor is not None else
self.y_range[2] / 2)
self.n_repeats = n_repeats
self.virtual_time = virtual_time
self.max_anchors_per_line = max_anchors_per_line
self.padding = padding
self.stroke_width = stroke_width
half_noise = self.noise_factor / 2
np.random.seed(0)
start_points = np.array(
[(x - half_noise) * RIGHT + (y - half_noise) * UP +
(z - half_noise) * OUT + self.noise_factor * np.random.random(3)
for n in range(self.n_repeats) for x in np.arange(*self.x_range)
for y in np.arange(*self.y_range)
for z in np.arange(*self.z_range)], )
def outside_box(p):
return (p[0] < self.x_range[0] - self.padding
or p[0] > self.x_range[1] + self.padding - self.x_range[2]
or p[1] < self.y_range[0] - self.padding
or p[1] > self.y_range[1] + self.padding - self.y_range[2]
or p[2] < self.z_range[0] - self.padding
or p[2] > self.z_range[1] + self.padding - self.z_range[2])
max_steps = ceil(virtual_time / dt) + 1
if not self.single_color:
self.background_img = self.get_colored_background_image()
if config["renderer"] == "opengl":
self.values_to_rgbas = self.get_vectorized_rgba_gradient_function(
min_color_scheme_value,
max_color_scheme_value,
colors,
)
for point in start_points:
points = [point]
for _ in range(max_steps):
last_point = points[-1]
new_point = last_point + dt * func(last_point)
if outside_box(new_point):
break
points.append(new_point)
step = max_steps
if not step:
continue
if config["renderer"] == "opengl":
line = OpenGLVMobject()
else:
line = VMobject()
line.duration = step * dt
step = max(1, int(len(points) / self.max_anchors_per_line))
line.set_points_smoothly(points[::step])
if self.single_color:
line.set_stroke(self.color)
else:
if config["renderer"] == "opengl":
# scaled for compatibility with cairo
line.set_stroke(width=self.stroke_width / 4.0)
norms = np.array([
np.linalg.norm(self.func(point))
for point in line.points
], )
line.set_rgba_array_direct(
self.values_to_rgbas(norms, opacity),
name="stroke_rgba",
)
else:
if np.any(self.z_range != np.array([0, 0.5, 0.5])):
line.set_stroke(
[self.pos_to_color(p)
for p in line.get_anchors()], )
else:
line.color_using_background_image(self.background_img)
line.set_stroke(width=self.stroke_width, opacity=opacity)
self.add(line)
self.stream_lines = [*self.submobjects]